Water · Worked step by step
How many gallons are in 500 feet of 24 inch main?
If math has never been your thing, you are in the right place. Try it on paper first, then we write it out with you, one small step at a time, and explain every step in plain words so you never lose the thread.
The problem
A transmission main is 24 inches across and 500 feet long. How many gallons does it hold when full?
Grab a pen and paper first
Give it a real try on paper before you watch. If you get stuck, take a hint. If you go blank, that is fine, press play and we will walk it through together.
Watch it solved, with you
Every step is written out slowly and explained in plain words, so you always know what just happened. Nobody skips ahead and leaves you behind.
Press play and I’ll write it out with you, one small step at a time.
Every step gets a plain-words explanation here, so you always know exactly what just happened and why.
The written version, step by step
- 1
Change inches to feet
across = 24 in = 2 ft
- 24 divided by 12 is 2 feet.
- So the main is 2 feet across.
- Now everything is in feet.
- 2
Find the circle end
area = 0.785 × 2 × 2 • area = 3.14 sq ft
- Circle end = 0.785 times across times across.
- 2 times 2 is 4.
- 4 times 0.785 is 3.14 square feet.
- 3
Times length, then gallons
cubic feet = 3.14 × 500 = 1,570 • gallons = 1,570 × 7.48 = 11,744
- Multiply the circle by the 500 foot length: 1,570 cubic feet.
- Then times 7.48 for gallons.
- About 11,744 gallons.
Quick trick: Estimate: 1,570 × 7.5 is about 11,775. Right there.
Remember this for good
A 24-inch main is exactly 2 feet across, so the circle end is 0.785 × 2 × 2 = 3.14 square feet.
24 inches is 2 feet. Circle end 3.14 sq ft, times the length, times 7.48. Big mains hold a lot.
Solve it fast next time
- Change inches to feet first: 24 divided by 12 is 2 ft.
- Pipe gallons = circle end times length times 7.48.
- A 2-foot pipe holds 3.14 square feet of water for every foot of length.
The answer: About 11,744 gallons.